(b) The machines (software + hardware) - through which the algorithms are implemented.

​Regarding
component (b) - it is undoubtedly artifical - a robotic arm (corporal extension) a GPU (hardware) or Python code (software) written to implement an algorithm -
is an artifical creation.

However, what about
component (a) - that is - the algorithms themselves?

One feature which, unarguably, does distinguish between components (a) and (b) - is the fact that the alghorithms themeselves are
abstract concepts while the artifical machines which implement them are, by definition,
not.

The question of wether abstract concepts discovered\described\developed by us are "artificial" - is not new - and in matheamtics has actually occupied generations - under the titile of the question "is mathematics discovered or invented?". Here are some radically different answers from some great thinkers:

In order to simplify also this question - note that our mathematical corpus is really made of a few components (a) Theorems (b) definitions (the objects which the theorems describe) and (c) Proofs. The real dispute of "invented vs. discovered" is about (b) and mainly (c). Indeed, clearly, Pythagoras Theorem is true because it is a
"static universal truth" - independently of Pythagoras and\or the proof which he gave. In this sense, the collection of these "universal truths" or "theorems" is probably most well described in terms of the views expressed by E. Frenkel (clip down to the left).

In fact, the collection of all such "theorems" is divided into two components - the theorems for which we know proofs and does for which we do not. The notion of such an abstract "collection" of theorems (with proofs) has been described rather poetically in the famous quote by great 20-th century mathematician Paul Erdos:

The question about "invention" is really relevant about how are new "definitions" introduced and how are proofs developed. And here, really, there seems to be an intermediary feature between "discovery" and "invention" - a "partnership" of a sort. In particualr, with respect to (b) and (c) the view seems aduqately described by the views expressed by S. Wolfram (clip down to the right). Invention could of course be replaced with the words "engineered" or "artifical". Invention is also "dynamic".

However, contarary to the algorithms , and, in particular, the AI algorithms, mathematical theorems are both "static" and indepndent of specific input. The AI algorithms, however, show us what they are capble of doing only once we give them input (millions of picures in different categories, text to analys, chess and go champions to compete against, etc...). In particular, since the only way we can implement these algorithms is through the machines - it seems to us that the machines are an essential part of the AI algorithm or in other words that the "machine is learning" - while in fact it is the
algorithm that does the learning - the machine only facilitates the abstract algorithm.

In particular, when it comes to the statical mathematical counterparts of "theorems" we have already graduated to viewing them as having an "abstract existence" by their own. That is - Pyhtogras theorem is valid as an abstract truth - without requiring us to draw a corporal triangle.

This actually leads to the following very interesting question:

Question: Can the AI algorithms be viewed as abstract concepts - which exist independently of the artifical machines which implement them?

In fact, the idea that such "abstract intelligence" exist is actually far from new and has been suggested, for instance, in the writings of Aristotle under the term "active intellect".

​

"T
his sort of intellect [which is like light in the way it makes potential things work as what they are] is separate, as well as being without attributes and unmixedsince it is by its thinghood a being-at-work, for what acts is always distinguished in stature above what is acted upon, as a governing source is above the material it works on.

Knowledge (epistēmē), in its being-at-work, is the same as the thing it knows, and while knowledge in potency comes first in time in any one knower, in the whole of things it does not take precedence even in time.

This does not mean that at one time it thinks but at another time it does not think, but when separated it is just exactly what it is, and this alone is deathless and everlasting (though we have no memory, because this sort of intellect is not acted upon, while the sort that is acted upon is destructible), and without this nothing thinks.

" (Aristotle - De Anime III)​​

This idea of "abstract intellects" was mentioned in various other sources and writings. For instance Maimonides

"Everything created in the world is divided into three parts: some creatures composed of corpus and form existing and decaying always like bodies of men, beast, vegetative and metals some creatures which are composed of corpus and form and are not changing from body to body etc and
some creatures which are form without any corpus etc..." (Maimonides - Foundations - 2:5)"
(Maimonides - Foundations - 2:3)

However, Maimonides also goes further from Aristotle - as according to his view - there should also be a
hierarchy among such "intellects".

"And in what would the forms be seperated one from the other - as they are not corporal? Because they are not equal in their reality but each one is below the stature of its friend and it is found from its power one above the other etc and that we have said one below its friend, is not the stature of place like man that sits above his friend, but
like is said in two sages that one is greater than his friend in wisdom that he is above the stature of the other, and like is said that the cause is above its effect"
(Maimonides - Foundations - 2:5-6)

In this sense

(1) The intellect underlying AI might not only be non-artificial but actually viewed as a "universal abstraction" - somewhat like the "static" Pythagoras theorem.

(2) The machine - is not the one doing the learning - but is only viewed as a vessel for uncovering the nature and capabilities of the "abstract intellect" or the "AI algorithm". (like smoke for a laser beam).

Last, somewhat optimistic:

(3) Some leading individuals have latelay expressed their concerns and worries that AI might lead for grave implications for humanity (Elon Musk, Hawking, ...) - for instance the effects on works, science, art etc... However, if we do accept the idea that "AI intellect" might have a "hierarchy" - it might be that just the fact that we have uncovered "intellects" - which can play chess, go, atari games... do music, recognize dogs and cats, sceince...better than us - doesn't mean we have uncovered the "highest" of these intellects - maybe the AI intellects we were capable to discover so far - are actually only the lowest rungs (even though they play atari really good)? Maybe the scientific thinking patterns - which we view as the peak would be found to be not the final rung. In this sense - there might still be what to discover.

In conclusion, let's go back to the question in the interview with E. Frenkel about "discovery vs. invention":

"Because if mathematics exists outside of space and time and outside of logic what else is out there" (E. Frenkel - Interview)